[Footnote 15: Aristot. Analyt. Post. I. iii. p. 72, b. 5-p. 73, a. 20: [Greek: ô(/st' e)peidê\ _o)li/ga toiau=ta_ e)n tai=s a)podei/xesin], &c.] Demonstrative Science is attained only by syllogizing from necessary premisses, such as cannot possibly be other than they are. The predicate must be (1) _de omni_, (2) _per se_, (3) _quatenus ipsum_, so that it is a _Primum Universale_; this third characteristic not being realized without the preceding two. First, the predicate must belong, and belong at all times, to everything called by the name of the subject. Next, it must belong thereunto _per se_, or essentially; that is, either the predicate must be stated in the definition declaring the essence of the subject, or the subject must be stated in the definition declaring the essence of the predicate. The predicate must not be extra-essential to the subject, nor attached to it as an adjunct from without, simply concomitant or accidental. The like distinction holds in regard to events: some are accidentally concomitant sequences which may or may not be realized (_e.g._, a flash of lightning occurring when a man is on his journey); in others, the conjunction is necessary or causal (as when an animal dies under the sacrificial knife).[16] Both these two characteristics (_de omni_ and _per se_) are presupposed in the third (_quatenus ipsum_); but this last implies farther, that the predicate is attached to the subject in the highest universality consistent with truth; _i.e._, that it is a First Universal, a primary predicate and not a derivative predicate. Thus, the predicate of having its three angles equal to two right angles, is a characteristic not merely _de omni_ and _per se_, but also a First Universal, applied to a triangle. It is applied to a triangle, _quatenus_ triangle, as a primary predicate. If applied to a subject of higher universality (_e.g._, to every geometrical figure), it would not be always true. If applied to a subject of lower universality (_e.g._, to a right-angled triangle or an isosceles triangle), it would be universally true and would be true _per se_, but it would be a derivative predicate and not a First Universal; it would not be applied to the isosceles _quatenus_ isosceles, for there is a still higher Universal of which it is predicable, being true respecting any triangle you please. Thus, the properties with which Demonstration, or full and absolute Science, is conversant, are _de omni_, _per se_, and _quatenus ipsum_, or _Universalia Prima_;[17] all of them necessary, such as cannot but be true.] [Footnote 16: Aristot. Analyt. Post. I. iv. p. 73, a. 21, b. 16.